Initial revision

Originally committed as revision 2 to svn://svn.ffmpeg.org/ffmpeg/trunk

1 files changed, 1584 insertions, 0 deletions

diff --git a/libav/jrevdct.c b/libav/jrevdct.c
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+/*
+ * jrevdct.c
+ *
+ * Copyright (C) 1991, 1992, Thomas G. Lane.
+ * This file is part of the Independent JPEG Group's software.
+ * For conditions of distribution and use, see the accompanying README file.
+ *
+ * This file contains the basic inverse-DCT transformation subroutine.
+ *
+ * This implementation is based on an algorithm described in
+ *   C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1-D DCT
+ *   Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics,
+ *   Speech, and Signal Processing 1989 (ICASSP '89), pp. 988-991.
+ * The primary algorithm described there uses 11 multiplies and 29 adds.
+ * We use their alternate method with 12 multiplies and 32 adds.
+ * The advantage of this method is that no data path contains more than one
+ * multiplication; this allows a very simple and accurate implementation in
+ * scaled fixed-point arithmetic, with a minimal number of shifts.
+ *
+ * I've made lots of modifications to attempt to take advantage of the
+ * sparse nature of the DCT matrices we're getting.  Although the logic
+ * is cumbersome, it's straightforward and the resulting code is much
+ * faster.
+ *
+ * A better way to do this would be to pass in the DCT block as a sparse
+ * matrix, perhaps with the difference cases encoded.
+ */
+
+typedef int INT32;
+
+/* Definition of Contant integer scale factor. */
+#define CONST_BITS 13
+
+/* Misc DCT definitions */
+#define DCTSIZE		8	/* The basic DCT block is 8x8 samples */
+#define DCTSIZE2	64	/* DCTSIZE squared; # of elements in a block */
+
+#define GLOBAL			/* a function referenced thru EXTERNs */
+
+typedef int DCTELEM;
+typedef DCTELEM DCTBLOCK[DCTSIZE2];
+
+void j_rev_dct (DCTELEM *data);
+
+
+#define GLOBAL			/* a function referenced thru EXTERNs */
+#define ORIG_DCT	1
+
+/* We assume that right shift corresponds to signed division by 2 with
+ * rounding towards minus infinity.  This is correct for typical "arithmetic
+ * shift" instructions that shift in copies of the sign bit.  But some
+ * C compilers implement >> with an unsigned shift.  For these machines you
+ * must define RIGHT_SHIFT_IS_UNSIGNED.
+ * RIGHT_SHIFT provides a proper signed right shift of an INT32 quantity.
+ * It is only applied with constant shift counts.  SHIFT_TEMPS must be
+ * included in the variables of any routine using RIGHT_SHIFT.
+ */
+
+#ifdef RIGHT_SHIFT_IS_UNSIGNED
+#define SHIFT_TEMPS	INT32 shift_temp;
+#define RIGHT_SHIFT(x,shft)  \
+	((shift_temp = (x)) < 0 ? \
+	 (shift_temp >> (shft)) | ((~((INT32) 0)) << (32-(shft))) : \
+	 (shift_temp >> (shft)))
+#else
+#define SHIFT_TEMPS
+#define RIGHT_SHIFT(x,shft)	((x) >> (shft))
+#endif
+
+/*
+ * This routine is specialized to the case DCTSIZE = 8.
+ */
+
+#if DCTSIZE != 8
+  Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
+#endif
+
+
+/*
+ * A 2-D IDCT can be done by 1-D IDCT on each row followed by 1-D IDCT
+ * on each column.  Direct algorithms are also available, but they are
+ * much more complex and seem not to be any faster when reduced to code.
+ *
+ * The poop on this scaling stuff is as follows:
+ *
+ * Each 1-D IDCT step produces outputs which are a factor of sqrt(N)
+ * larger than the true IDCT outputs.  The final outputs are therefore
+ * a factor of N larger than desired; since N=8 this can be cured by
+ * a simple right shift at the end of the algorithm.  The advantage of
+ * this arrangement is that we save two multiplications per 1-D IDCT,
+ * because the y0 and y4 inputs need not be divided by sqrt(N).
+ *
+ * We have to do addition and subtraction of the integer inputs, which
+ * is no problem, and multiplication by fractional constants, which is
+ * a problem to do in integer arithmetic.  We multiply all the constants
+ * by CONST_SCALE and convert them to integer constants (thus retaining
+ * CONST_BITS bits of precision in the constants).  After doing a
+ * multiplication we have to divide the product by CONST_SCALE, with proper
+ * rounding, to produce the correct output.  This division can be done
+ * cheaply as a right shift of CONST_BITS bits.  We postpone shifting
+ * as long as possible so that partial sums can be added together with
+ * full fractional precision.
+ *
+ * The outputs of the first pass are scaled up by PASS1_BITS bits so that
+ * they are represented to better-than-integral precision.  These outputs
+ * require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word
+ * with the recommended scaling.  (To scale up 12-bit sample data further, an
+ * intermediate INT32 array would be needed.)
+ *
+ * To avoid overflow of the 32-bit intermediate results in pass 2, we must
+ * have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26.  Error analysis
+ * shows that the values given below are the most effective.
+ */
+
+#ifdef EIGHT_BIT_SAMPLES
+#define PASS1_BITS  2
+#else
+#define PASS1_BITS  1		/* lose a little precision to avoid overflow */
+#endif
+
+#define ONE	((INT32) 1)
+
+#define CONST_SCALE (ONE << CONST_BITS)
+
+/* Convert a positive real constant to an integer scaled by CONST_SCALE.
+ * IMPORTANT: if your compiler doesn't do this arithmetic at compile time,
+ * you will pay a significant penalty in run time.  In that case, figure
+ * the correct integer constant values and insert them by hand.
+ */
+
+#define FIX(x)	((INT32) ((x) * CONST_SCALE + 0.5))
+
+/* Descale and correctly round an INT32 value that's scaled by N bits.
+ * We assume RIGHT_SHIFT rounds towards minus infinity, so adding
+ * the fudge factor is correct for either sign of X.
+ */
+
+#define DESCALE(x,n)  RIGHT_SHIFT((x) + (ONE << ((n)-1)), n)
+#define SCALE(x,n)	((INT32)(x) << n)
+
+/* Multiply an INT32 variable by an INT32 constant to yield an INT32 result.
+ * For 8-bit samples with the recommended scaling, all the variable
+ * and constant values involved are no more than 16 bits wide, so a
+ * 16x16->32 bit multiply can be used instead of a full 32x32 multiply;
+ * this provides a useful speedup on many machines.
+ * There is no way to specify a 16x16->32 multiply in portable C, but
+ * some C compilers will do the right thing if you provide the correct
+ * combination of casts.
+ * NB: for 12-bit samples, a full 32-bit multiplication will be needed.
+ */
+
+#ifdef EIGHT_BIT_SAMPLES
+#ifdef SHORTxSHORT_32		/* may work if 'int' is 32 bits */
+#define MULTIPLY(var,const)  (((INT16) (var)) * ((INT16) (const)))
+#endif
+#ifdef SHORTxLCONST_32		/* known to work with Microsoft C 6.0 */
+#define MULTIPLY(var,const)  (((INT16) (var)) * ((INT32) (const)))
+#endif
+#endif
+
+#if 0
+/* force a multiplication for x86 where a multiply is fast). We
+   force the non constant operand to be in a register because
+   otherwise it may be a 16 bit memory reference, which is not allowed
+   by imull */
+#define MULTIPLY(a,b) \
+({\
+    int res;\
+    asm("imull %2,%1,%0" : "=r" (res) : "r" ((int)(a)), "i" (b));\
+    res;\
+})
+#endif
+
+#ifndef MULTIPLY		/* default definition */
+#define MULTIPLY(var,const)  ((var) * (const))
+#endif
+
+
+#ifndef ORIG_DCT
+
+#undef SSMUL
+#define SSMUL(var1,var2)  ((INT16)(var1) * (INT32)(INT16)(var2))
+
+/* Precomputed idct value arrays. */
+
+STATIC DCTELEM PreIDCT[64][64];
+
+/* Pre compute singleton coefficient IDCT values. */
+void init_pre_idct() {
+    int i;
+
+    for (i = 0; i < 64; i++) {
+	memset ((char *) PreIDCT[i], 0, 64 * sizeof(DCTELEM));
+	PreIDCT[i][i] = 2048;
+	j_rev_dct (PreIDCT[i]);
+    }
+}
+
+/*
+ * Perform the inverse DCT on one block of coefficients.
+ */
+
+void j_rev_dct_sparse (data, pos)
+	DCTBLOCK data;
+	int pos;
+{
+    register DCTELEM *dataptr;
+    short int val;
+    DCTELEM *ndataptr;
+    int coeff, rr;
+
+    /* If DC Coefficient. */
+
+    if (pos == 0) {
+	register INT32 *dp;
+	register INT32 v;
+
+	dp = (INT32*)data;
+	v = *data;
+	/* Compute 32 bit value to assign.
+	 *  This speeds things up a bit */
+	if (v < 0)
+	    val = (short)((v - 3) >> 3);
+	else
+	    val = (short)((v + 4) >> 3);
+	v = val | ((INT32)val << 16);
+	dp[0] = v;      dp[1] = v;      dp[2] = v;      dp[3] = v;
+	dp[4] = v;      dp[5] = v;      dp[6] = v;      dp[7] = v;
+	dp[8] = v;      dp[9] = v;      dp[10] = v;     dp[11] = v;
+	dp[12] = v;     dp[13] = v;     dp[14] = v;     dp[15] = v;
+	dp[16] = v;     dp[17] = v;     dp[18] = v;     dp[19] = v;
+	dp[20] = v;     dp[21] = v;     dp[22] = v;     dp[23] = v;
+	dp[24] = v;     dp[25] = v;     dp[26] = v;     dp[27] = v;
+	dp[28] = v;     dp[29] = v;     dp[30] = v;     dp[31] = v;
+	return;
+    }
+
+    /* Some other coefficient. */
+    dataptr = (DCTELEM *)data;
+    coeff = dataptr[pos];
+    ndataptr = PreIDCT[pos];
+
+    for (rr = 0; rr < 4; rr++) {
+	dataptr[0]  = (DCTELEM)(SSMUL (ndataptr[0] , coeff) >> (CONST_BITS-2));
+	dataptr[1]  = (DCTELEM)(SSMUL (ndataptr[1] , coeff) >> (CONST_BITS-2));
+	dataptr[2]  = (DCTELEM)(SSMUL (ndataptr[2] , coeff) >> (CONST_BITS-2));
+	dataptr[3]  = (DCTELEM)(SSMUL (ndataptr[3] , coeff) >> (CONST_BITS-2));
+	dataptr[4]  = (DCTELEM)(SSMUL (ndataptr[4] , coeff) >> (CONST_BITS-2));
+	dataptr[5]  = (DCTELEM)(SSMUL (ndataptr[5] , coeff) >> (CONST_BITS-2));
+	dataptr[6]  = (DCTELEM)(SSMUL (ndataptr[6] , coeff) >> (CONST_BITS-2));
+	dataptr[7]  = (DCTELEM)(SSMUL (ndataptr[7] , coeff) >> (CONST_BITS-2));
+	dataptr[8]  = (DCTELEM)(SSMUL (ndataptr[8] , coeff) >> (CONST_BITS-2));
+	dataptr[9]  = (DCTELEM)(SSMUL (ndataptr[9] , coeff) >> (CONST_BITS-2));
+	dataptr[10] = (DCTELEM)(SSMUL (ndataptr[10], coeff) >> (CONST_BITS-2));
+	dataptr[11] = (DCTELEM)(SSMUL (ndataptr[11], coeff) >> (CONST_BITS-2));
+	dataptr[12] = (DCTELEM)(SSMUL (ndataptr[12], coeff) >> (CONST_BITS-2));
+	dataptr[13] = (DCTELEM)(SSMUL (ndataptr[13], coeff) >> (CONST_BITS-2));
+	dataptr[14] = (DCTELEM)(SSMUL (ndataptr[14], coeff) >> (CONST_BITS-2));
+	dataptr[15] = (DCTELEM)(SSMUL (ndataptr[15], coeff) >> (CONST_BITS-2));
+	dataptr += 16;
+	ndataptr += 16;
+    }
+}
+
+
+void j_rev_dct (data)
+	DCTBLOCK data;
+{
+    INT32 tmp0, tmp1, tmp2, tmp3;
+    INT32 tmp10, tmp11, tmp12, tmp13;
+    INT32 z1, z2, z3, z4, z5;
+    int d0, d1, d2, d3, d4, d5, d6, d7;
+    register DCTELEM *dataptr;
+    int rowctr;
+    SHIFT_TEMPS;
+
+    /* Pass 1: process rows. */
+    /* Note results are scaled up by sqrt(8) compared to a true IDCT; */
+    /* furthermore, we scale the results by 2**PASS1_BITS. */
+
+    dataptr = data;
+
+    for (rowctr = DCTSIZE - 1; rowctr >= 0; rowctr--) {
+	/* Due to quantization, we will usually find that many of the input
+	 * coefficients are zero, especially the AC terms.  We can exploit this
+	 * by short-circuiting the IDCT calculation for any row in which all
+	 * the AC terms are zero.  In that case each output is equal to the
+	 * DC coefficient (with scale factor as needed).
+	 * With typical images and quantization tables, half or more of the
+	 * row DCT calculations can be simplified this way.
+	 */
+
+	register INT32 *idataptr = (INT32*)dataptr;
+	d0 = dataptr[0];
+	d1 = dataptr[1];
+	if ((d1 == 0) && (idataptr[1] | idataptr[2] | idataptr[3]) == 0) {
+	    /* AC terms all zero */
+	    if (d0) {
+		/* Compute a 32 bit value to assign. */
+		DCTELEM dcval = (DCTELEM) (d0 << PASS1_BITS);
+		register INT32 v = (dcval & 0xffff) |
+				   (((INT32)dcval << 16) & 0xffff0000L);
+
+		idataptr[0] = v;
+		idataptr[1] = v;
+		idataptr[2] = v;
+		idataptr[3] = v;
+	    }
+
+	    dataptr += DCTSIZE;	/* advance pointer to next row */
+	    continue;
+	}
+	d2 = dataptr[2];
+	d3 = dataptr[3];
+	d4 = dataptr[4];
+	d5 = dataptr[5];
+	d6 = dataptr[6];
+	d7 = dataptr[7];
+
+	/* Even part: reverse the even part of the forward DCT. */
+	/* The rotator is sqrt(2)*c(-6). */
+	if (d6) {
+	    if (d4) {
+		if (d2) {
+		    if (d0) {
+			/* d0 != 0, d2 != 0, d4 != 0, d6 != 0 */
+			z1 = MULTIPLY(d2 + d6, FIX(0.541196100));
+			tmp2 = z1 + MULTIPLY(d6, - FIX(1.847759065));
+			tmp3 = z1 + MULTIPLY(d2, FIX(0.765366865));
+
+			tmp0 = SCALE (d0 + d4, CONST_BITS);
+			tmp1 = SCALE (d0 - d4, CONST_BITS);
+
+			tmp10 = tmp0 + tmp3;
+			tmp13 = tmp0 - tmp3;
+			tmp11 = tmp1 + tmp2;
+			tmp12 = tmp1 - tmp2;
+		    } else {
+			/* d0 == 0, d2 != 0, d4 != 0, d6 != 0 */
+			z1 = MULTIPLY(d2 + d6, FIX(0.541196100));
+			tmp2 = z1 + MULTIPLY(d6, - FIX(1.847759065));
+			tmp3 = z1 + MULTIPLY(d2, FIX(0.765366865));
+
+			tmp0 = SCALE (d4, CONST_BITS);
+
+			tmp10 = tmp0 + tmp3;
+			tmp13 = tmp0 - tmp3;
+			tmp11 = tmp2 - tmp0;
+			tmp12 = -(tmp0 + tmp2);
+		    }
+		} else {
+		    if (d0) {
+			/* d0 != 0, d2 == 0, d4 != 0, d6 != 0 */
+			tmp2 = MULTIPLY(d6, - FIX(1.306562965));
+			tmp3 = MULTIPLY(d6, FIX(0.541196100));
+
+			tmp0 = SCALE (d0 + d4, CONST_BITS);
+			tmp1 = SCALE (d0 - d4, CONST_BITS);
+
+			tmp10 = tmp0 + tmp3;
+			tmp13 = tmp0 - tmp3;
+			tmp11 = tmp1 + tmp2;
+			tmp12 = tmp1 - tmp2;
+		    } else {
+			/* d0 == 0, d2 == 0, d4 != 0, d6 != 0 */
+			tmp2 = MULTIPLY(d6, -FIX(1.306562965));
+			tmp3 = MULTIPLY(d6, FIX(0.541196100));
+
+			tmp0 = SCALE (d4, CONST_BITS);
+
+			tmp10 = tmp0 + tmp3;
+			tmp13 = tmp0 - tmp3;
+			tmp11 = tmp2 - tmp0;
+			tmp12 = -(tmp0 + tmp2);
+		    }
+		}
+	    } else {
+		if (d2) {
+		    if (d0) {
+			/* d0 != 0, d2 != 0, d4 == 0, d6 != 0 */
+			z1 = MULTIPLY(d2 + d6, FIX(0.541196100));
+			tmp2 = z1 + MULTIPLY(d6, - FIX(1.847759065));
+			tmp3 = z1 + MULTIPLY(d2, FIX(0.765366865));
+
+			tmp0 = SCALE (d0, CONST_BITS);
+
+			tmp10 = tmp0 + tmp3;
+			tmp13 = tmp0 - tmp3;
+			tmp11 = tmp0 + tmp2;
+			tmp12 = tmp0 - tmp2;
+		    } else {
+			/* d0 == 0, d2 != 0, d4 == 0, d6 != 0 */
+			z1 = MULTIPLY(d2 + d6, FIX(0.541196100));
+			tmp2 = z1 + MULTIPLY(d6, - FIX(1.847759065));
+			tmp3 = z1 + MULTIPLY(d2, FIX(0.765366865));
+
+			tmp10 = tmp3;
+			tmp13 = -tmp3;
+			tmp11 = tmp2;
+			tmp12 = -tmp2;
+		    }
+		} else {
+		    if (d0) {
+			/* d0 != 0, d2 == 0, d4 == 0, d6 != 0 */
+			tmp2 = MULTIPLY(d6, - FIX(1.306562965));
+			tmp3 = MULTIPLY(d6, FIX(0.541196100));
+
+			tmp0 = SCALE (d0, CONST_BITS);
+
+			tmp10 = tmp0 + tmp3;
+			tmp13 = tmp0 - tmp3;
+			tmp11 = tmp0 + tmp2;
+			tmp12 = tmp0 - tmp2;
+		    } else {
+			/* d0 == 0, d2 == 0, d4 == 0, d6 != 0 */
+			tmp2 = MULTIPLY(d6, - FIX(1.306562965));
+			tmp3 = MULTIPLY(d6, FIX(0.541196100));
+
+			tmp10 = tmp3;
+			tmp13 = -tmp3;
+			tmp11 = tmp2;
+			tmp12 = -tmp2;
+		    }
+		}
+	    }
+	} else {
+	    if (d4) {
+		if (d2) {
+		    if (d0) {
+			/* d0 != 0, d2 != 0, d4 != 0, d6 == 0 */
+			tmp2 = MULTIPLY(d2, FIX(0.541196100));
+			tmp3 = MULTIPLY(d2, FIX(1.306562965));
+
+			tmp0 = SCALE (d0 + d4, CONST_BITS);
+			tmp1 = SCALE (d0 - d4, CONST_BITS);
+
+			tmp10 = tmp0 + tmp3;
+			tmp13 = tmp0 - tmp3;
+			tmp11 = tmp1 + tmp2;
+			tmp12 = tmp1 - tmp2;
+		    } else {
+			/* d0 == 0, d2 != 0, d4 != 0, d6 == 0 */
+			tmp2 = MULTIPLY(d2, FIX(0.541196100));
+			tmp3 = MULTIPLY(d2, FIX(1.306562965));
+
+			tmp0 = SCALE (d4, CONST_BITS);
+
+			tmp10 = tmp0 + tmp3;
+			tmp13 = tmp0 - tmp3;
+			tmp11 = tmp2 - tmp0;
+			tmp12 = -(tmp0 + tmp2);
+		    }
+		} else {
+		    if (d0) {
+			/* d0 != 0, d2 == 0, d4 != 0, d6 == 0 */
+			tmp10 = tmp13 = SCALE (d0 + d4, CONST_BITS);
+			tmp11 = tmp12 = SCALE (d0 - d4, CONST_BITS);
+		    } else {
+			/* d0 == 0, d2 == 0, d4 != 0, d6 == 0 */
+			tmp10 = tmp13 = SCALE (d4, CONST_BITS);
+			tmp11 = tmp12 = -tmp10;
+		    }
+		}
+	    } else {
+		if (d2) {
+		    if (d0) {
+			/* d0 != 0, d2 != 0, d4 == 0, d6 == 0 */
+			tmp2 = MULTIPLY(d2, FIX(0.541196100));
+			tmp3 = MULTIPLY(d2, FIX(1.306562965));
+
+			tmp0 = SCALE (d0, CONST_BITS);
+
+			tmp10 = tmp0 + tmp3;
+			tmp13 = tmp0 - tmp3;
+			tmp11 = tmp0 + tmp2;
+			tmp12 = tmp0 - tmp2;
+		    } else {
+			/* d0 == 0, d2 != 0, d4 == 0, d6 == 0 */
+			tmp2 = MULTIPLY(d2, FIX(0.541196100));
+			tmp3 = MULTIPLY(d2, FIX(1.306562965));
+
+			tmp10 = tmp3;
+			tmp13 = -tmp3;
+			tmp11 = tmp2;
+			tmp12 = -tmp2;
+		    }
+		} else {
+		    if (d0) {
+			/* d0 != 0, d2 == 0, d4 == 0, d6 == 0 */
+			tmp10 = tmp13 = tmp11 = tmp12 = SCALE (d0, CONST_BITS);
+		    } else {
+			/* d0 == 0, d2 == 0, d4 == 0, d6 == 0 */
+			tmp10 = tmp13 = tmp11 = tmp12 = 0;
+		    }
+		}
+	    }
+	}
+
+
+	/* Odd part per figure 8; the matrix is unitary and hence its
+	 * transpose is its inverse.  i0..i3 are y7,y5,y3,y1 respectively.
+	 */
+
+	if (d7) {
+	    if (d5) {
+		if (d3) {
+		    if (d1) {
+			/* d1 != 0, d3 != 0, d5 != 0, d7 != 0 */
+			z1 = d7 + d1;
+			z2 = d5 + d3;
+			z3 = d7 + d3;
+			z4 = d5 + d1;
+			z5 = MULTIPLY(z3 + z4, FIX(1.175875602));
+
+			tmp0 = MULTIPLY(d7, FIX(0.298631336));
+			tmp1 = MULTIPLY(d5, FIX(2.053119869));
+			tmp2 = MULTIPLY(d3, FIX(3.072711026));
+			tmp3 = MULTIPLY(d1, FIX(1.501321110));
+			z1 = MULTIPLY(z1, - FIX(0.899976223));
+			z2 = MULTIPLY(z2, - FIX(2.562915447));
+			z3 = MULTIPLY(z3, - FIX(1.961570560));
+			z4 = MULTIPLY(z4, - FIX(0.390180644));
+
+			z3 += z5;
+			z4 += z5;
+
+			tmp0 += z1 + z3;
+			tmp1 += z2 + z4;
+			tmp2 += z2 + z3;
+			tmp3 += z1 + z4;
+		    } else {
+			/* d1 == 0, d3 != 0, d5 != 0, d7 != 0 */
+			z1 = d7;
+			z2 = d5 + d3;
+			z3 = d7 + d3;
+			z5 = MULTIPLY(z3 + d5, FIX(1.175875602));
+
+			tmp0 = MULTIPLY(d7, FIX(0.298631336));
+			tmp1 = MULTIPLY(d5, FIX(2.053119869));
+			tmp2 = MULTIPLY(d3, FIX(3.072711026));
+			z1 = MULTIPLY(d7, - FIX(0.899976223));
+			z2 = MULTIPLY(z2, - FIX(2.562915447));
+			z3 = MULTIPLY(z3, - FIX(1.961570560));
+			z4 = MULTIPLY(d5, - FIX(0.390180644));
+
+			z3 += z5;
+			z4 += z5;
+
+			tmp0 += z1 + z3;
+			tmp1 += z2 + z4;
+			tmp2 += z2 + z3;
+			tmp3 = z1 + z4;
+		    }
+		} else {
+		    if (d1) {
+			/* d1 != 0, d3 == 0, d5 != 0, d7 != 0 */
+			z1 = d7 + d1;
+			z2 = d5;
+			z3 = d7;
+			z4 = d5 + d1;
+			z5 = MULTIPLY(z3 + z4, FIX(1.175875602));
+
+			tmp0 = MULTIPLY(d7, FIX(0.298631336));
+			tmp1 = MULTIPLY(d5, FIX(2.053119869));
+			tmp3 = MULTIPLY(d1, FIX(1.501321110));
+			z1 = MULTIPLY(z1, - FIX(0.899976223));
+			z2 = MULTIPLY(d5, - FIX(2.562915447));
+			z3 = MULTIPLY(d7, - FIX(1.961570560));
+			z4 = MULTIPLY(z4, - FIX(0.390180644));
+
+			z3 += z5;
+			z4 += z5;
+
+			tmp0 += z1 + z3;
+			tmp1 += z2 + z4;
+			tmp2 = z2 + z3;
+			tmp3 += z1 + z4;
+		    } else {
+			/* d1 == 0, d3 == 0, d5 != 0, d7 != 0 */
+			tmp0 = MULTIPLY(d7, - FIX(0.601344887));
+			z1 = MULTIPLY(d7, - FIX(0.899976223));
+			z3 = MULTIPLY(d7, - FIX(1.961570560));
+			tmp1 = MULTIPLY(d5, - FIX(0.509795578));
+			z2 = MULTIPLY(d5, - FIX(2.562915447));
+			z4 = MULTIPLY(d5, - FIX(0.390180644));
+			z5 = MULTIPLY(d5 + d7, FIX(1.175875602));
+
+			z3 += z5;
+			z4 += z5;
+
+			tmp0 += z3;
+			tmp1 += z4;
+			tmp2 = z2 + z3;
+			tmp3 = z1 + z4;
+		    }
+		}
+	    } else {
+		if (d3) {
+		    if (d1) {
+			/* d1 != 0, d3 != 0, d5 == 0, d7 != 0 */
+			z1 = d7 + d1;
+			z3 = d7 + d3;
+			z5 = MULTIPLY(z3 + d1, FIX(1.175875602));
+
+			tmp0 = MULTIPLY(d7, FIX(0.298631336));
+			tmp2 = MULTIPLY(d3, FIX(3.072711026));
+			tmp3 = MULTIPLY(d1, FIX(1.501321110));
+			z1 = MULTIPLY(z1, - FIX(0.899976223));
+			z2 = MULTIPLY(d3, - FIX(2.562915447));
+			z3 = MULTIPLY(z3, - FIX(1.961570560));
+			z4 = MULTIPLY(d1, - FIX(0.390180644));
+
+			z3 += z5;
+			z4 += z5;
+
+			tmp0 += z1 + z3;
+			tmp1 = z2 + z4;
+			tmp2 += z2 + z3;
+			tmp3 += z1 + z4;
+		    } else {
+			/* d1 == 0, d3 != 0, d5 == 0, d7 != 0 */
+			z3 = d7 + d3;
+
+			tmp0 = MULTIPLY(d7, - FIX(0.601344887));
+			z1 = MULTIPLY(d7, - FIX(0.899976223));
+			tmp2 = MULTIPLY(d3, FIX(0.509795579));
+			z2 = MULTIPLY(d3, - FIX(2.562915447));
+			z5 = MULTIPLY(z3, FIX(1.175875602));
+			z3 = MULTIPLY(z3, - FIX(0.785694958));
+
+			tmp0 += z3;
+			tmp1 = z2 + z5;
+			tmp2 += z3;
+			tmp3 = z1 + z5;
+		    }
+		} else {
+		    if (d1) {
+			/* d1 != 0, d3 == 0, d5 == 0, d7 != 0 */
+			z1 = d7 + d1;
+			z5 = MULTIPLY(z1, FIX(1.175875602));
+
+			z1 = MULTIPLY(z1, FIX(0.275899379));
+			z3 = MULTIPLY(d7, - FIX(1.961570560));
+			tmp0 = MULTIPLY(d7, - FIX(1.662939224));
+			z4 = MULTIPLY(d1, - FIX(0.390180644));
+			tmp3 = MULTIPLY(d1, FIX(1.111140466));
+
+			tmp0 += z1;
+			tmp1 = z4 + z5;
+			tmp2 = z3 + z5;
+			tmp3 += z1;
+		    } else {
+			/* d1 == 0, d3 == 0, d5 == 0, d7 != 0 */
+			tmp0 = MULTIPLY(d7, - FIX(1.387039845));
+			tmp1 = MULTIPLY(d7, FIX(1.175875602));
+			tmp2 = MULTIPLY(d7, - FIX(0.785694958));
+			tmp3 = MULTIPLY(d7, FIX(0.275899379));
+		    }
+		}
+	    }
+	} else {
+	    if (d5) {
+		if (d3) {
+		    if (d1) {
+			/* d1 != 0, d3 != 0, d5 != 0, d7 == 0 */
+			z2 = d5 + d3;
+			z4 = d5 + d1;
+			z5 = MULTIPLY(d3 + z4, FIX(1.175875602));
+
+			tmp1 = MULTIPLY(d5, FIX(2.053119869));
+			tmp2 = MULTIPLY(d3, FIX(3.072711026));
+			tmp3 = MULTIPLY(d1, FIX(1.501321110));
+			z1 = MULTIPLY(d1, - FIX(0.899976223));
+			z2 = MULTIPLY(z2, - FIX(2.562915447));
+			z3 = MULTIPLY(d3, - FIX(1.961570560));
+			z4 = MULTIPLY(z4, - FIX(0.390180644));
+
+			z3 += z5;
+			z4 += z5;
+
+			tmp0 = z1 + z3;
+			tmp1 += z2 + z4;
+			tmp2 += z2 + z3;
+			tmp3 += z1 + z4;
+		    } else {
+			/* d1 == 0, d3 != 0, d5 != 0, d7 == 0 */
+			z2 = d5 + d3;
+
+			z5 = MULTIPLY(z2, FIX(1.175875602));
+			tmp1 = MULTIPLY(d5, FIX(1.662939225));
+			z4 = MULTIPLY(d5, - FIX(0.390180644));
+			z2 = MULTIPLY(z2, - FIX(1.387039845));
+			tmp2 = MULTIPLY(d3, FIX(1.111140466));
+			z3 = MULTIPLY(d3, - FIX(1.961570560));
+
+			tmp0 = z3 + z5;
+			tmp1 += z2;
+			tmp2 += z2;
+			tmp3 = z4 + z5;
+		    }
+		} else {
+		    if (d1) {
+			/* d1 != 0, d3 == 0, d5 != 0, d7 == 0 */
+			z4 = d5 + d1;
+
+			z5 = MULTIPLY(z4, FIX(1.175875602));
+			z1 = MULTIPLY(d1, - FIX(0.899976223));
+			tmp3 = MULTIPLY(d1, FIX(0.601344887));
+			tmp1 = MULTIPLY(d5, - FIX(0.509795578));
+			z2 = MULTIPLY(d5, - FIX(2.562915447));
+			z4 = MULTIPLY(z4, FIX(0.785694958));
+
+			tmp0 = z1 + z5;
+			tmp1 += z4;
+			tmp2 = z2 + z5;
+			tmp3 += z4;
+		    } else {
+			/* d1 == 0, d3 == 0, d5 != 0, d7 == 0 */
+			tmp0 = MULTIPLY(d5, FIX(1.175875602));
+			tmp1 = MULTIPLY(d5, FIX(0.275899380));
+			tmp2 = MULTIPLY(d5, - FIX(1.387039845));
+			tmp3 = MULTIPLY(d5, FIX(0.785694958));
+		    }
+		}
+	    } else {
+		if (d3) {
+		    if (d1) {
+			/* d1 != 0, d3 != 0, d5 == 0, d7 == 0 */
+			z5 = d1 + d3;
+			tmp3 = MULTIPLY(d1, FIX(0.211164243));
+			tmp2 = MULTIPLY(d3, - FIX(1.451774981));
+			z1 = MULTIPLY(d1, FIX(1.061594337));
+			z2 = MULTIPLY(d3, - FIX(2.172734803));
+			z4 = MULTIPLY(z5, FIX(0.785694958));
+			z5 = MULTIPLY(z5, FIX(1.175875602));
+
+			tmp0 = z1 - z4;
+			tmp1 = z2 + z4;
+			tmp2 += z5;
+			tmp3 += z5;
+		    } else {
+			/* d1 == 0, d3 != 0, d5 == 0, d7 == 0 */
+			tmp0 = MULTIPLY(d3, - FIX(0.785694958));
+			tmp1 = MULTIPLY(d3, - FIX(1.387039845));
+			tmp2 = MULTIPLY(d3, - FIX(0.275899379));
+			tmp3 = MULTIPLY(d3, FIX(1.175875602));
+		    }
+		} else {
+		    if (d1) {
+			/* d1 != 0, d3 == 0, d5 == 0, d7 == 0 */
+			tmp0 = MULTIPLY(d1, FIX(0.275899379));
+			tmp1 = MULTIPLY(d1, FIX(0.785694958));
+			tmp2 = MULTIPLY(d1, FIX(1.175875602));
+			tmp3 = MULTIPLY(d1, FIX(1.387039845));
+		    } else {
+			/* d1 == 0, d3 == 0, d5 == 0, d7 == 0 */
+			tmp0 = tmp1 = tmp2 = tmp3 = 0;
+		    }
+		}
+	    }
+	}
+
+	/* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */
+
+	dataptr[0] = (DCTELEM) DESCALE(tmp10 + tmp3, CONST_BITS-PASS1_BITS);
+	dataptr[7] = (DCTELEM) DESCALE(tmp10 - tmp3, CONST_BITS-PASS1_BITS);
+	dataptr[1] = (DCTELEM) DESCALE(tmp11 + tmp2, CONST_BITS-PASS1_BITS);
+	dataptr[6] = (DCTELEM) DESCALE(tmp11 - tmp2, CONST_BITS-PASS1_BITS);
+	dataptr[2] = (DCTELEM) DESCALE(tmp12 + tmp1, CONST_BITS-PASS1_BITS);
+	dataptr[5] = (DCTELEM) DESCALE(tmp12 - tmp1, CONST_BITS-PASS1_BITS);
+	dataptr[3] = (DCTELEM) DESCALE(tmp13 + tmp0, CONST_BITS-PASS1_BITS);
+	dataptr[4] = (DCTELEM) DESCALE(tmp13 - tmp0, CONST_BITS-PASS1_BITS);
+
+	dataptr += DCTSIZE;		/* advance pointer to next row */
+    }
+
+    /* Pass 2: process columns. */
+    /* Note that we must descale the results by a factor of 8 == 2**3, */
+    /* and also undo the PASS1_BITS scaling. */
+
+    dataptr = data;
+    for (rowctr = DCTSIZE-1; rowctr >= 0; rowctr--) {
+	/* Columns of zeroes can be exploited in the same way as we did with rows.
+	 * However, the row calculation has created many nonzero AC terms, so the
+	 * simplification applies less often (typically 5% to 10% of the time).
+	 * On machines with very fast multiplication, it's possible that the
+	 * test takes more time than it's worth.  In that case this section
+	 * may be commented out.
+	 */
+
+	d0 = dataptr[DCTSIZE*0];
+	d1 = dataptr[DCTSIZE*1];
+	d2 = dataptr[DCTSIZE*2];
+	d3 = dataptr[DCTSIZE*3];
+	d4 = dataptr[DCTSIZE*4];
+	d5 = dataptr[DCTSIZE*5];
+	d6 = dataptr[DCTSIZE*6];
+	d7 = dataptr[DCTSIZE*7];
+
+	/* Even part: reverse the even part of the forward DCT. */
+	/* The rotator is sqrt(2)*c(-6). */
+	if (d6) {
+	    if (d4) {
+		if (d2) {
+		    if (d0) {
+			/* d0 != 0, d2 != 0, d4 != 0, d6 != 0 */
+			z1 = MULTIPLY(d2 + d6, FIX(0.541196100));
+			tmp2 = z1 + MULTIPLY(d6, - FIX(1.847759065));
+			tmp3 = z1 + MULTIPLY(d2, FIX(0.765366865));
+
+			tmp0 = SCALE (d0 + d4, CONST_BITS);
+			tmp1 = SCALE (d0 - d4, CONST_BITS);
+
+			tmp10 = tmp0 + tmp3;
+			tmp13 = tmp0 - tmp3;
+			tmp11 = tmp1 + tmp2;
+			tmp12 = tmp1 - tmp2;
+		    } else {
+			/* d0 == 0, d2 != 0, d4 != 0, d6 != 0 */
+			z1 = MULTIPLY(d2 + d6, FIX(0.541196100));
+			tmp2 = z1 + MULTIPLY(d6, - FIX(1.847759065));
+			tmp3 = z1 + MULTIPLY(d2, FIX(0.765366865));
+
+			tmp0 = SCALE (d4, CONST_BITS);
+
+			tmp10 = tmp0 + tmp3;
+			tmp13 = tmp0 - tmp3;
+			tmp11 = tmp2 - tmp0;
+			tmp12 = -(tmp0 + tmp2);
+		    }
+		} else {
+		    if (d0) {
+			/* d0 != 0, d2 == 0, d4 != 0, d6 != 0 */
+			tmp2 = MULTIPLY(d6, - FIX(1.306562965));
+			tmp3 = MULTIPLY(d6, FIX(0.541196100));
+
+			tmp0 = SCALE (d0 + d4, CONST_BITS);
+			tmp1 = SCALE (d0 - d4, CONST_BITS);
+
+			tmp10 = tmp0 + tmp3;
+			tmp13 = tmp0 - tmp3;
+			tmp11 = tmp1 + tmp2;
+			tmp12 = tmp1 - tmp2;
+		    } else {
+			/* d0 == 0, d2 == 0, d4 != 0, d6 != 0 */
+			tmp2 = MULTIPLY(d6, -FIX(1.306562965));
+			tmp3 = MULTIPLY(d6, FIX(0.541196100));
+
+			tmp0 = SCALE (d4, CONST_BITS);
+
+			tmp10 = tmp0 + tmp3;
+			tmp13 = tmp0 - tmp3;
+			tmp11 = tmp2 - tmp0;
+			tmp12 = -(tmp0 + tmp2);
+		    }
+		}
+	    } else {
+		if (d2) {
+		    if (d0) {
+			/* d0 != 0, d2 != 0, d4 == 0, d6 != 0 */
+			z1 = MULTIPLY(d2 + d6, FIX(0.541196100));
+			tmp2 = z1 + MULTIPLY(d6, - FIX(1.847759065));
+			tmp3 = z1 + MULTIPLY(d2, FIX(0.765366865));
+
+			tmp0 = SCALE (d0, CONST_BITS);
+
+			tmp10 = tmp0 + tmp3;
+			tmp13 = tmp0 - tmp3;
+			tmp11 = tmp0 + tmp2;
+			tmp12 = tmp0 - tmp2;
+		    } else {
+			/* d0 == 0, d2 != 0, d4 == 0, d6 != 0 */
+			z1 = MULTIPLY(d2 + d6, FIX(0.541196100));
+			tmp2 = z1 + MULTIPLY(d6, - FIX(1.847759065));
+			tmp3 = z1 + MULTIPLY(d2, FIX(0.765366865));
+
+			tmp10 = tmp3;
+			tmp13 = -tmp3;
+			tmp11 = tmp2;
+			tmp12 = -tmp2;
+		    }
+		} else {
+		    if (d0) {
+			/* d0 != 0, d2 == 0, d4 == 0, d6 != 0 */
+			tmp2 = MULTIPLY(d6, - FIX(1.306562965));
+			tmp3 = MULTIPLY(d6, FIX(0.541196100));
+
+			tmp0 = SCALE (d0, CONST_BITS);
+
+			tmp10 = tmp0 + tmp3;
+			tmp13 = tmp0 - tmp3;
+			tmp11 = tmp0 + tmp2;
+			tmp12 = tmp0 - tmp2;
+		    } else {
+			/* d0 == 0, d2 == 0, d4 == 0, d6 != 0 */
+			tmp2 = MULTIPLY(d6, - FIX(1.306562965));
+			tmp3 = MULTIPLY(d6, FIX(0.541196100));
+
+			tmp10 = tmp3;
+			tmp13 = -tmp3;
+			tmp11 = tmp2;
+			tmp12 = -tmp2;
+		    }
+		}
+	    }
+	} else {
+	    if (d4) {
+		if (d2) {
+		    if (d0) {
+			/* d0 != 0, d2 != 0, d4 != 0, d6 == 0 */
+			tmp2 = MULTIPLY(d2, FIX(0.541196100));
+			tmp3 = MULTIPLY(d2, FIX(1.306562965));
+
+			tmp0 = SCALE (d0 + d4, CONST_BITS);
+			tmp1 = SCALE (d0 - d4, CONST_BITS);
+
+			tmp10 = tmp0 + tmp3;
+			tmp13 = tmp0 - tmp3;
+			tmp11 = tmp1 + tmp2;
+			tmp12 = tmp1 - tmp2;
+		    } else {
+			/* d0 == 0, d2 != 0, d4 != 0, d6 == 0 */
+			tmp2 = MULTIPLY(d2, FIX(0.541196100));
+			tmp3 = MULTIPLY(d2, FIX(1.306562965));
+
+			tmp0 = SCALE (d4, CONST_BITS);
+
+			tmp10 = tmp0 + tmp3;
+			tmp13 = tmp0 - tmp3;
+			tmp11 = tmp2 - tmp0;
+			tmp12 = -(tmp0 + tmp2);
+		    }
+		} else {
+		    if (d0) {
+			/* d0 != 0, d2 == 0, d4 != 0, d6 == 0 */
+			tmp10 = tmp13 = SCALE (d0 + d4, CONST_BITS);
+			tmp11 = tmp12 = SCALE (d0 - d4, CONST_BITS);
+		    } else {
+			/* d0 == 0, d2 == 0, d4 != 0, d6 == 0 */
+			tmp10 = tmp13 = SCALE (d4, CONST_BITS);
+			tmp11 = tmp12 = -tmp10;
+		    }
+		}
+	    } else {
+		if (d2) {
+		    if (d0) {
+			/* d0 != 0, d2 != 0, d4 == 0, d6 == 0 */
+			tmp2 = MULTIPLY(d2, FIX(0.541196100));
+			tmp3 = MULTIPLY(d2, FIX(1.306562965));
+
+			tmp0 = SCALE (d0, CONST_BITS);
+
+			tmp10 = tmp0 + tmp3;
+			tmp13 = tmp0 - tmp3;
+			tmp11 = tmp0 + tmp2;
+			tmp12 = tmp0 - tmp2;
+		    } else {
+			/* d0 == 0, d2 != 0, d4 == 0, d6 == 0 */
+			tmp2 = MULTIPLY(d2, FIX(0.541196100));
+			tmp3 = MULTIPLY(d2, FIX(1.306562965));
+
+			tmp10 = tmp3;
+			tmp13 = -tmp3;
+			tmp11 = tmp2;
+			tmp12 = -tmp2;
+		    }
+		} else {
+		    if (d0) {
+			/* d0 != 0, d2 == 0, d4 == 0, d6 == 0 */
+			tmp10 = tmp13 = tmp11 = tmp12 = SCALE (d0, CONST_BITS);
+		    } else {
+			/* d0 == 0, d2 == 0, d4 == 0, d6 == 0 */
+			tmp10 = tmp13 = tmp11 = tmp12 = 0;
+		    }
+		}
+	    }
+	}
+
+	/* Odd part per figure 8; the matrix is unitary and hence its
+	 * transpose is its inverse.  i0..i3 are y7,y5,y3,y1 respectively.
+	 */
+	if (d7) {
+	    if (d5) {
+		if (d3) {
+		    if (d1) {
+			/* d1 != 0, d3 != 0, d5 != 0, d7 != 0 */
+			z1 = d7 + d1;
+			z2 = d5 + d3;
+			z3 = d7 + d3;
+			z4 = d5 + d1;
+			z5 = MULTIPLY(z3 + z4, FIX(1.175875602));
+
+			tmp0 = MULTIPLY(d7, FIX(0.298631336));
+			tmp1 = MULTIPLY(d5, FIX(2.053119869));
+			tmp2 = MULTIPLY(d3, FIX(3.072711026));
+			tmp3 = MULTIPLY(d1, FIX(1.501321110));
+			z1 = MULTIPLY(z1, - FIX(0.899976223));
+			z2 = MULTIPLY(z2, - FIX(2.562915447));
+			z3 = MULTIPLY(z3, - FIX(1.961570560));
+			z4 = MULTIPLY(z4, - FIX(0.390180644));
+
+			z3 += z5;
+			z4 += z5;
+
+			tmp0 += z1 + z3;
+			tmp1 += z2 + z4;
+			tmp2 += z2 + z3;
+			tmp3 += z1 + z4;
+		    } else {
+			/* d1 == 0, d3 != 0, d5 != 0, d7 != 0 */
+			z1 = d7;
+			z2 = d5 + d3;
+			z3 = d7 + d3;
+			z5 = MULTIPLY(z3 + d5, FIX(1.175875602));
+
+			tmp0 = MULTIPLY(d7, FIX(0.298631336));
+			tmp1 = MULTIPLY(d5, FIX(2.053119869));
+			tmp2 = MULTIPLY(d3, FIX(3.072711026));
+			z1 = MULTIPLY(d7, - FIX(0.899976223));
+			z2 = MULTIPLY(z2, - FIX(2.562915447));
+			z3 = MULTIPLY(z3, - FIX(1.961570560));
+			z4 = MULTIPLY(d5, - FIX(0.390180644));
+
+			z3 += z5;
+			z4 += z5;
+
+			tmp0 += z1 + z3;
+			tmp1 += z2 + z4;
+			tmp2 += z2 + z3;
+			tmp3 = z1 + z4;
+		    }
+		} else {
+		    if (d1) {
+			/* d1 != 0, d3 == 0, d5 != 0, d7 != 0 */
+			z1 = d7 + d1;
+			z2 = d5;
+			z3 = d7;
+			z4 = d5 + d1;
+			z5 = MULTIPLY(z3 + z4, FIX(1.175875602));
+
+			tmp0 = MULTIPLY(d7, FIX(0.298631336));
+			tmp1 = MULTIPLY(d5, FIX(2.053119869));
+			tmp3 = MULTIPLY(d1, FIX(1.501321110));
+			z1 = MULTIPLY(z1, - FIX(0.899976223));
+			z2 = MULTIPLY(d5, - FIX(2.562915447));
+			z3 = MULTIPLY(d7, - FIX(1.961570560));
+			z4 = MULTIPLY(z4, - FIX(0.390180644));
+
+			z3 += z5;
+			z4 += z5;
+
+			tmp0 += z1 + z3;
+			tmp1 += z2 + z4;
+			tmp2 = z2 + z3;
+			tmp3 += z1 + z4;
+		    } else {
+			/* d1 == 0, d3 == 0, d5 != 0, d7 != 0 */
+			tmp0 = MULTIPLY(d7, - FIX(0.601344887));
+			z1 = MULTIPLY(d7, - FIX(0.899976223));
+			z3 = MULTIPLY(d7, - FIX(1.961570560));
+			tmp1 = MULTIPLY(d5, - FIX(0.509795578));
+			z2 = MULTIPLY(d5, - FIX(2.562915447));
+			z4 = MULTIPLY(d5, - FIX(0.390180644));
+			z5 = MULTIPLY(d5 + d7, FIX(1.175875602));
+
+			z3 += z5;
+			z4 += z5;
+
+			tmp0 += z3;
+			tmp1 += z4;
+			tmp2 = z2 + z3;
+			tmp3 = z1 + z4;
+		    }
+		}
+	    } else {
+		if (d3) {
+		    if (d1) {
+			/* d1 != 0, d3 != 0, d5 == 0, d7 != 0 */
+			z1 = d7 + d1;
+			z3 = d7 + d3;
+			z5 = MULTIPLY(z3 + d1, FIX(1.175875602));
+
+			tmp0 = MULTIPLY(d7, FIX(0.298631336));
+			tmp2 = MULTIPLY(d3, FIX(3.072711026));
+			tmp3 = MULTIPLY(d1, FIX(1.501321110));
+			z1 = MULTIPLY(z1, - FIX(0.899976223));
+			z2 = MULTIPLY(d3, - FIX(2.562915447));
+			z3 = MULTIPLY(z3, - FIX(1.961570560));
+			z4 = MULTIPLY(d1, - FIX(0.390180644));
+
+			z3 += z5;
+			z4 += z5;
+
+			tmp0 += z1 + z3;
+			tmp1 = z2 + z4;
+			tmp2 += z2 + z3;
+			tmp3 += z1 + z4;
+		    } else {
+			/* d1 == 0, d3 != 0, d5 == 0, d7 != 0 */
+			z3 = d7 + d3;
+
+			tmp0 = MULTIPLY(d7, - FIX(0.601344887));
+			z1 = MULTIPLY(d7, - FIX(0.899976223));
+			tmp2 = MULTIPLY(d3, FIX(0.509795579));
+			z2 = MULTIPLY(d3, - FIX(2.562915447));
+			z5 = MULTIPLY(z3, FIX(1.175875602));
+			z3 = MULTIPLY(z3, - FIX(0.785694958));
+
+			tmp0 += z3;
+			tmp1 = z2 + z5;
+			tmp2 += z3;
+			tmp3 = z1 + z5;
+		    }
+		} else {
+		    if (d1) {
+			/* d1 != 0, d3 == 0, d5 == 0, d7 != 0 */
+			z1 = d7 + d1;
+			z5 = MULTIPLY(z1, FIX(1.175875602));
+
+			z1 = MULTIPLY(z1, FIX(0.275899379));
+			z3 = MULTIPLY(d7, - FIX(1.961570560));
+			tmp0 = MULTIPLY(d7, - FIX(1.662939224));
+			z4 = MULTIPLY(d1, - FIX(0.390180644));
+			tmp3 = MULTIPLY(d1, FIX(1.111140466));
+
+			tmp0 += z1;
+			tmp1 = z4 + z5;
+			tmp2 = z3 + z5;
+			tmp3 += z1;
+		    } else {
+			/* d1 == 0, d3 == 0, d5 == 0, d7 != 0 */
+			tmp0 = MULTIPLY(d7, - FIX(1.387039845));
+			tmp1 = MULTIPLY(d7, FIX(1.175875602));
+			tmp2 = MULTIPLY(d7, - FIX(0.785694958));
+			tmp3 = MULTIPLY(d7, FIX(0.275899379));
+		    }
+		}
+	    }
+	} else {
+	    if (d5) {
+		if (d3) {
+		    if (d1) {
+			/* d1 != 0, d3 != 0, d5 != 0, d7 == 0 */
+			z2 = d5 + d3;
+			z4 = d5 + d1;
+			z5 = MULTIPLY(d3 + z4, FIX(1.175875602));
+
+			tmp1 = MULTIPLY(d5, FIX(2.053119869));
+			tmp2 = MULTIPLY(d3, FIX(3.072711026));
+			tmp3 = MULTIPLY(d1, FIX(1.501321110));
+			z1 = MULTIPLY(d1, - FIX(0.899976223));
+			z2 = MULTIPLY(z2, - FIX(2.562915447));
+			z3 = MULTIPLY(d3, - FIX(1.961570560));
+			z4 = MULTIPLY(z4, - FIX(0.390180644));
+
+			z3 += z5;
+			z4 += z5;
+
+			tmp0 = z1 + z3;
+			tmp1 += z2 + z4;
+			tmp2 += z2 + z3;
+			tmp3 += z1 + z4;
+		    } else {
+			/* d1 == 0, d3 != 0, d5 != 0, d7 == 0 */
+			z2 = d5 + d3;
+
+			z5 = MULTIPLY(z2, FIX(1.175875602));
+			tmp1 = MULTIPLY(d5, FIX(1.662939225));
+			z4 = MULTIPLY(d5, - FIX(0.390180644));
+			z2 = MULTIPLY(z2, - FIX(1.387039845));
+			tmp2 = MULTIPLY(d3, FIX(1.111140466));
+			z3 = MULTIPLY(d3, - FIX(1.961570560));
+
+			tmp0 = z3 + z5;
+			tmp1 += z2;
+			tmp2 += z2;
+			tmp3 = z4 + z5;
+		    }
+		} else {
+		    if (d1) {
+			/* d1 != 0, d3 == 0, d5 != 0, d7 == 0 */
+			z4 = d5 + d1;
+
+			z5 = MULTIPLY(z4, FIX(1.175875602));
+			z1 = MULTIPLY(d1, - FIX(0.899976223));
+			tmp3 = MULTIPLY(d1, FIX(0.601344887));
+			tmp1 = MULTIPLY(d5, - FIX(0.509795578));
+			z2 = MULTIPLY(d5, - FIX(2.562915447));
+			z4 = MULTIPLY(z4, FIX(0.785694958));
+
+			tmp0 = z1 + z5;
+			tmp1 += z4;
+			tmp2 = z2 + z5;
+			tmp3 += z4;
+		    } else {
+			/* d1 == 0, d3 == 0, d5 != 0, d7 == 0 */
+			tmp0 = MULTIPLY(d5, FIX(1.175875602));
+			tmp1 = MULTIPLY(d5, FIX(0.275899380));
+			tmp2 = MULTIPLY(d5, - FIX(1.387039845));
+			tmp3 = MULTIPLY(d5, FIX(0.785694958));
+		    }
+		}
+	    } else {
+		if (d3) {
+		    if (d1) {
+			/* d1 != 0, d3 != 0, d5 == 0, d7 == 0 */
+			z5 = d1 + d3;
+			tmp3 = MULTIPLY(d1, FIX(0.211164243));
+			tmp2 = MULTIPLY(d3, - FIX(1.451774981));
+			z1 = MULTIPLY(d1, FIX(1.061594337));
+			z2 = MULTIPLY(d3, - FIX(2.172734803));
+			z4 = MULTIPLY(z5, FIX(0.785694958));
+			z5 = MULTIPLY(z5, FIX(1.175875602));
+
+			tmp0 = z1 - z4;
+			tmp1 = z2 + z4;
+			tmp2 += z5;
+			tmp3 += z5;
+		    } else {
+			/* d1 == 0, d3 != 0, d5 == 0, d7 == 0 */
+			tmp0 = MULTIPLY(d3, - FIX(0.785694958));
+			tmp1 = MULTIPLY(d3, - FIX(1.387039845));
+			tmp2 = MULTIPLY(d3, - FIX(0.275899379));
+			tmp3 = MULTIPLY(d3, FIX(1.175875602));
+		    }
+		} else {
+		    if (d1) {
+			/* d1 != 0, d3 == 0, d5 == 0, d7 == 0 */
+			tmp0 = MULTIPLY(d1, FIX(0.275899379));
+			tmp1 = MULTIPLY(d1, FIX(0.785694958));
+			tmp2 = MULTIPLY(d1, FIX(1.175875602));
+			tmp3 = MULTIPLY(d1, FIX(1.387039845));
+		    } else {
+			/* d1 == 0, d3 == 0, d5 == 0, d7 == 0 */
+			tmp0 = tmp1 = tmp2 = tmp3 = 0;
+		    }
+		}
+	    }
+	}
+
+	/* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */
+
+	dataptr[DCTSIZE*0] = (DCTELEM) DESCALE(tmp10 + tmp3,
+	    CONST_BITS+PASS1_BITS+3);
+	dataptr[DCTSIZE*7] = (DCTELEM) DESCALE(tmp10 - tmp3,
+	    CONST_BITS+PASS1_BITS+3);
+	dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp11 + tmp2,
+	    CONST_BITS+PASS1_BITS+3);
+	dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(tmp11 - tmp2,
+	    CONST_BITS+PASS1_BITS+3);
+	dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(tmp12 + tmp1,
+	    CONST_BITS+PASS1_BITS+3);
+	dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp12 - tmp1,
+	    CONST_BITS+PASS1_BITS+3);
+	dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(tmp13 + tmp0,
+	    CONST_BITS+PASS1_BITS+3);
+	dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp13 - tmp0,
+	    CONST_BITS+PASS1_BITS+3);
+
+	dataptr++;			/* advance pointer to next column */
+    }
+}
+
+#else
+
+/*---- debugging/tracing macros ----*/
+
+#if _MSC_VER
+#pragma optimize("",on)
+#if _MSC_VER > 700
+/*#pragma optimize("l",off)*/
+#endif
+#endif
+
+#define idct_single_pos0()
+#define idct_zero_col_stat()
+#define idct_zero_row_stat()
+#define idct_nonzero_col_stat()
+#define idct_nonzero_row_stat()
+#define DUMP_COEFS(p)
+#define TRACE(args)
+#define FAST_DCTPTRS	1
+
+#if 0	/* to count cases */
+void idct_single_pos0 (void) { static int count; count++; }
+void idct_zero_col_stat (void) { static int count; count++; }
+void idct_zero_row_stat (void) { static int count; count++; }
+void idct_nonzero_col_stat (void) { static int count; count++; }
+void idct_nonzero_row_stat (void) { static int count; count++; }
+#undef idct_single_pos0
+#undef idct_zero_col_stat
+#undef idct_zero_row_stat
+#undef idct_nonzero_col_stat
+#undef idct_nonzero_row_stat
+#endif
+
+void init_pre_idct (void) { }
+
+void j_rev_dct_sparse (DCTBLOCK data, int pos)
+{
+    /* If just DC Coefficient. */
+
+    if (pos == 0) {
+	register DCTELEM *dp, *dq;
+	DCTELEM dcval;
+
+	idct_single_pos0();
+
+	dp = data;
+	dcval = dp[0];
+	if (dcval < 0)
+	    dcval = (short)((dcval - 3) >> 3);
+	else
+	    dcval = (short)((dcval + 4) >> 3);
+
+	if (dcval) {
+	    for (dq = dp + 64; dp < dq; dp += 8) {
+		dp[3] = dp[2] = dp[1] = dp[0] = dcval;
+		dp[7] = dp[6] = dp[5] = dp[4] = dcval;
+	    }
+	}
+	return;
+    }
+
+    /* Some other coeff */
+    j_rev_dct (data);
+}
+
+#ifndef OPTIMIZE_ASM
+void j_rev_dct (DCTBLOCK data)
+{
+    INT32 tmp0, tmp1, tmp2, tmp3;
+    INT32 tmp10, tmp11, tmp12, tmp13;
+    INT32 z1, z2, z3, z4, z5;
+    register DCTELEM *dp;
+    int rowctr;
+    SHIFT_TEMPS;
+
+    /* Pass 1: process rows. */
+    /* Note results are scaled up by sqrt(8) compared to a true IDCT; */
+    /* furthermore, we scale the results by 2**PASS1_BITS. */
+
+    DUMP_COEFS(data);
+
+    dp = data;
+    for (rowctr = DCTSIZE-1; rowctr >= 0; rowctr--, dp += DCTSIZE) {
+	/* Due to quantization, we will usually find that many of the input
+	 * coefficients are zero, especially the AC terms.  We can exploit this
+	 * by short-circuiting the IDCT calculation for any row in which all
+	 * the AC terms are zero.  In that case each output is equal to the
+	 * DC coefficient (with scale factor as needed).
+	 * With typical images and quantization tables, half or more of the
+	 * row DCT calculations can be simplified this way.
+	 */
+
+#if FAST_DCTPTRS
+#define d0	dp[0]
+#define d1	dp[1]
+#define d2	dp[2]
+#define d3	dp[3]
+#define d4	dp[4]
+#define d5	dp[5]
+#define d6	dp[6]
+#define d7	dp[7]
+#else
+	int d0 = dp[0];
+	int d1 = dp[1];
+	int d2 = dp[2];
+	int d3 = dp[3];
+	int d4 = dp[4];
+	int d5 = dp[5];
+	int d6 = dp[6];
+	int d7 = dp[7];
+#endif
+
+#ifndef NO_ZERO_ROW_TEST
+	if ((d1 | d2 | d3 | d4 | d5 | d6 | d7) == 0) {
+	    /* AC terms all zero */
+	    DCTELEM dcval = (DCTELEM) (d0 << PASS1_BITS);
+
+	    if (d0) {
+		dp[0] = dcval;
+		dp[1] = dcval;
+		dp[2] = dcval;
+		dp[3] = dcval;
+		dp[4] = dcval;
+		dp[5] = dcval;
+		dp[6] = dcval;
+		dp[7] = dcval;
+	    }
+	    idct_zero_row_stat();
+	    continue;
+	}
+#endif
+
+	idct_nonzero_row_stat();
+
+	/* Even part: reverse the even part of the forward DCT. */
+	/* The rotator is sqrt(2)*c(-6). */
+
+	z1 = MULTIPLY(d2 + d6, FIX(0.541196100));
+	tmp2 = z1 + MULTIPLY(d6, - FIX(1.847759065));
+	tmp3 = z1 + MULTIPLY(d2, FIX(0.765366865));
+
+	tmp0 = SCALE (d0 + d4, CONST_BITS);
+	tmp1 = SCALE (d0 - d4, CONST_BITS);
+
+	tmp10 = tmp0 + tmp3;
+	tmp13 = tmp0 - tmp3;
+	tmp11 = tmp1 + tmp2;
+	tmp12 = tmp1 - tmp2;
+
+	/* Odd part per figure 8; the matrix is unitary and hence its
+	 * transpose is its inverse.  i0..i3 are y7,y5,y3,y1 respectively.
+	 */
+
+	z1 = d7 + d1;
+	z2 = d5 + d3;
+	z3 = d7 + d3;
+	z4 = d5 + d1;
+	z5 = MULTIPLY(z3 + z4, FIX(1.175875602)); /* sqrt(2) * c3 */
+
+	tmp0 = MULTIPLY(d7, FIX(0.298631336)); /* sqrt(2) * (-c1+c3+c5-c7) */
+	tmp1 = MULTIPLY(d5, FIX(2.053119869)); /* sqrt(2) * ( c1+c3-c5+c7) */
+	tmp2 = MULTIPLY(d3, FIX(3.072711026)); /* sqrt(2) * ( c1+c3+c5-c7) */
+	tmp3 = MULTIPLY(d1, FIX(1.501321110)); /* sqrt(2) * ( c1+c3-c5-c7) */
+	z1 = MULTIPLY(z1, - FIX(0.899976223)); /* sqrt(2) * (c7-c3) */
+	z2 = MULTIPLY(z2, - FIX(2.562915447)); /* sqrt(2) * (-c1-c3) */
+	z3 = MULTIPLY(z3, - FIX(1.961570560)); /* sqrt(2) * (-c3-c5) */
+	z4 = MULTIPLY(z4, - FIX(0.390180644)); /* sqrt(2) * (c5-c3) */
+
+	z3 += z5;
+	z4 += z5;
+
+	tmp0 += z1 + z3;
+	tmp1 += z2 + z4;
+	tmp2 += z2 + z3;
+	tmp3 += z1 + z4;
+
+	/* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */
+
+	dp[0] = (DCTELEM) DESCALE(tmp10 + tmp3, CONST_BITS-PASS1_BITS);
+	dp[7] = (DCTELEM) DESCALE(tmp10 - tmp3, CONST_BITS-PASS1_BITS);
+	dp[1] = (DCTELEM) DESCALE(tmp11 + tmp2, CONST_BITS-PASS1_BITS);
+	dp[6] = (DCTELEM) DESCALE(tmp11 - tmp2, CONST_BITS-PASS1_BITS);
+	dp[2] = (DCTELEM) DESCALE(tmp12 + tmp1, CONST_BITS-PASS1_BITS);
+	dp[5] = (DCTELEM) DESCALE(tmp12 - tmp1, CONST_BITS-PASS1_BITS);
+	dp[3] = (DCTELEM) DESCALE(tmp13 + tmp0, CONST_BITS-PASS1_BITS);
+	dp[4] = (DCTELEM) DESCALE(tmp13 - tmp0, CONST_BITS-PASS1_BITS);
+    }
+#if FAST_DCTPTRS
+#undef d0
+#undef d1
+#undef d2
+#undef d3
+#undef d4
+#undef d5
+#undef d6
+#undef d7
+#endif
+
+    /* Pass 2: process columns. */
+    /* Note that we must descale the results by a factor of 8 == 2**3, */
+    /* and also undo the PASS1_BITS scaling. */
+
+    dp = data;
+    for (rowctr = DCTSIZE-1; rowctr >= 0; rowctr--, dp++) {
+	/* Columns of zeroes can be exploited in the same way as we did with rows.
+	 * However, the row calculation has created many nonzero AC terms, so the
+	 * simplification applies less often (typically 5% to 10% of the time).
+	 * On machines with very fast multiplication, it's possible that the
+	 * test takes more time than it's worth.  In that case this section
+	 * may be commented out.
+	 */
+
+#if FAST_DCTPTRS
+#define d0	dp[DCTSIZE*0]
+#define d1	dp[DCTSIZE*1]
+#define d2	dp[DCTSIZE*2]
+#define d3	dp[DCTSIZE*3]
+#define d4	dp[DCTSIZE*4]
+#define d5	dp[DCTSIZE*5]
+#define d6	dp[DCTSIZE*6]
+#define d7	dp[DCTSIZE*7]
+#else
+	int d0 = dp[DCTSIZE*0];
+	int d1 = dp[DCTSIZE*1];
+	int d2 = dp[DCTSIZE*2];
+	int d3 = dp[DCTSIZE*3];
+	int d4 = dp[DCTSIZE*4];
+	int d5 = dp[DCTSIZE*5];
+	int d6 = dp[DCTSIZE*6];
+	int d7 = dp[DCTSIZE*7];
+#endif
+
+#ifndef NO_ZERO_COLUMN_TEST
+	if ((d1 | d2 | d3 | d4 | d5 | d6 | d7) == 0) {
+	    /* AC terms all zero */
+	    DCTELEM dcval = (DCTELEM) DESCALE((INT32) d0, PASS1_BITS+3);
+
+	    if (d0) {
+		dp[DCTSIZE*0] = dcval;
+		dp[DCTSIZE*1] = dcval;
+		dp[DCTSIZE*2] = dcval;
+		dp[DCTSIZE*3] = dcval;
+		dp[DCTSIZE*4] = dcval;
+		dp[DCTSIZE*5] = dcval;
+		dp[DCTSIZE*6] = dcval;
+		dp[DCTSIZE*7] = dcval;
+	    }
+	    idct_zero_col_stat();
+	    continue;
+	}
+#endif
+
+	idct_nonzero_col_stat();
+
+	/* Even part: reverse the even part of the forward DCT. */
+	/* The rotator is sqrt(2)*c(-6). */
+
+	z1 = MULTIPLY(d2 + d6, FIX(0.541196100));
+	tmp2 = z1 + MULTIPLY(d6, - FIX(1.847759065));
+	tmp3 = z1 + MULTIPLY(d2, FIX(0.765366865));
+
+	tmp0 = SCALE (d0 + d4, CONST_BITS);
+	tmp1 = SCALE (d0 - d4, CONST_BITS);
+
+	tmp10 = tmp0 + tmp3;
+	tmp13 = tmp0 - tmp3;
+	tmp11 = tmp1 + tmp2;
+	tmp12 = tmp1 - tmp2;
+
+	/* Odd part per figure 8; the matrix is unitary and hence its
+	 * transpose is its inverse.  i0..i3 are y7,y5,y3,y1 respectively.
+	 */
+
+	z1 = d7 + d1;
+	z2 = d5 + d3;
+	z3 = d7 + d3;
+	z4 = d5 + d1;
+	z5 = MULTIPLY(z3 + z4, FIX(1.175875602)); /* sqrt(2) * c3 */
+
+	tmp0 = MULTIPLY(d7, FIX(0.298631336)); /* sqrt(2) * (-c1+c3+c5-c7) */
+	tmp1 = MULTIPLY(d5, FIX(2.053119869)); /* sqrt(2) * ( c1+c3-c5+c7) */
+	tmp2 = MULTIPLY(d3, FIX(3.072711026)); /* sqrt(2) * ( c1+c3+c5-c7) */
+	tmp3 = MULTIPLY(d1, FIX(1.501321110)); /* sqrt(2) * ( c1+c3-c5-c7) */
+	z1 = MULTIPLY(z1, - FIX(0.899976223)); /* sqrt(2) * (c7-c3) */
+	z2 = MULTIPLY(z2, - FIX(2.562915447)); /* sqrt(2) * (-c1-c3) */
+	z3 = MULTIPLY(z3, - FIX(1.961570560)); /* sqrt(2) * (-c3-c5) */
+	z4 = MULTIPLY(z4, - FIX(0.390180644)); /* sqrt(2) * (c5-c3) */
+
+	z3 += z5;
+	z4 += z5;
+
+	tmp0 += z1 + z3;
+	tmp1 += z2 + z4;
+	tmp2 += z2 + z3;
+	tmp3 += z1 + z4;
+
+	/* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */
+
+	dp[DCTSIZE*0] = (DCTELEM)DESCALE(tmp10 + tmp3, CONST_BITS+PASS1_BITS+3);
+	dp[DCTSIZE*7] = (DCTELEM)DESCALE(tmp10 - tmp3, CONST_BITS+PASS1_BITS+3);
+	dp[DCTSIZE*1] = (DCTELEM)DESCALE(tmp11 + tmp2, CONST_BITS+PASS1_BITS+3);
+	dp[DCTSIZE*6] = (DCTELEM)DESCALE(tmp11 - tmp2, CONST_BITS+PASS1_BITS+3);
+	dp[DCTSIZE*2] = (DCTELEM)DESCALE(tmp12 + tmp1, CONST_BITS+PASS1_BITS+3);
+	dp[DCTSIZE*5] = (DCTELEM)DESCALE(tmp12 - tmp1, CONST_BITS+PASS1_BITS+3);
+	dp[DCTSIZE*3] = (DCTELEM)DESCALE(tmp13 + tmp0, CONST_BITS+PASS1_BITS+3);
+	dp[DCTSIZE*4] = (DCTELEM)DESCALE(tmp13 - tmp0, CONST_BITS+PASS1_BITS+3);
+    }
+#if FAST_DCTPTRS
+#undef d0
+#undef d1
+#undef d2
+#undef d3
+#undef d4
+#undef d5
+#undef d6
+#undef d7
+#endif
+}
+#endif	/* optimize.asm */
+
+#endif